The PSD and Orifice Discharge in MSMA 2 OSD Calculation

For small developments (under 5 hectares), MSMA 2nd Edition provides a simplified calculation for On-Site Detention (OSD), where the design involves using pre-computed tables and figures (Table 5.A1, 5.A2, 5.A3, and 5.A4) to determine the permissible discharge (PSD), required storage volume (SSR) and the size of the inflow and outflow pipes. This method is a quick and easy way to design minor drainage systems specifically for 10-year ARI design storms, where engineers do not have to do detailed calculation and just extract the figures from the tables.

While MSMA guideline provided us with the PSD as a maximum allowable peak outflow, it did not indicate the calculation of orifice discharge using Equation 2.6 in MSMA.

 Q=Av=C_dA\sqrt{2gH_o}

Here, we go through Appendix 5.B (page 5-28), rework the example as per the table method and calculate the actual orifice discharge. We notice that the orifice discharge of the suggested outlet size is way bigger than the PSD obtained in the table. This is somehow inconsistent and questionable.

Result #

Another 5 sites of each region are selected and calculated to observe the PSD and the actual orifice discharge. All of the actual orifice discharge is way higher than the tabulated PSD as per table below.

File sample here

Information

Catchment area	: 0.8ha
Terrain type	: Mild
% Impervious area	: 90%
Outlet pipe position	: At the tank bottom

 

Effective head (H₀) = Height of storage – [Orifice Elevation from bottom of OSD + D₀/2]

 Orifice discharge (Q)=Av=C_dA\sqrt{2gH_o}

Hypothesis #

In order to achieve outlet discharge to be lesser than the PSD, we need to either set the outlet pipe invert level to be higher, or  reduce the outlet pipe diameter. In this section, we will adjust the effective head and outlet size, to get the orifice discharge similar to the PSD value, and observe the difference.

Adjust pipe invert level (i.e.: adjust effective head) #

The comparison was performed by adjusting the pipe invert level to be higher than the tank base, while keeping the pipe diameter as specified in the table.

To achieve the same discharge as the PSD, we find that we need to consistently reduce the effective head ( or make the pipe level higher than the storage Invert Level). There seems to be no regularity to how high the pipe level should be adjusted upwards.

Adjust outlet pipe diameter #

The comparison was carried out by adjusting the pipe diameter, while the pipe invert level was kept fixed at the tank bottom.

From the above comparison, to achieve the same discharge as the PSD, we will have to use a smaller orifice size, holding the effective head constant.

Conclusion #

PSD is consistently smaller than the orifice discharge in the sites that we chose for our study, assuming that the orifice is lying on the bottom of the OSD. It is not immediately clear how MSMA designers come up with how many percent the Orifice Discharge has to be reduced to give us the PSD, but it does seem that from our sample calculation, the PSD value is computed by reducing the orifice diameter size to 20% to 30%.